A Linear Prelle-Singer method

2024/05/13 by Duarte, L. G. S., Ferreira, H. S., da Mota, L. A. C. P.
#34-XX #Computational Physics (physics.comp-ph) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #G.1.7 #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2405.07912

Abstract

The Prelle-Singer method allows determining an elementary first integral admitted by a polynomial vector field in the plane. It is a semi-algorithm whose nonlinear step consists of determining the Darboux polynomials of the vector field. In this article we construct a linear procedure to determine the Darboux polynomials present in the integrating factor of a polynomial vector field in the plane. Next, we extend the procedure to deal with rational 2ODEs that admit an elementary first integral

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